Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 69Citation - Scopus: 73Classical and Fractional Aspects of Two Coupled Pendulums(Editura Acad Romane, 2019) Baleanu, D.; Baleanu, Dumitru; Jajarmi, A.; Asad, J. H.; MatematikIn this study, we consider two coupled pendulums (attached together with a spring) having the same length while the same masses are attached at their ends. After setting the system in motion we construct the classical Lagrangian, and as a result, we obtain the classical Euler-Lagrange equation. Then, we generalize the classical Lagrangian in order to derive the fractional Euler-Lagrange equation in the sense of two different fractional operators. Finally, we provide the numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on the Euler method to discretize the convolution integral. Numerical simulations show that the proposed approach is efficient and demonstrate new aspects of the real-world phenomena.Conference Object Path Integral Quantization of Brownian Motion as Mechanical Systems With Fractional Derivatives(IFAC Secretariat, 2006) Rabei, E.M.; Baleanu, D.; Muslih, S.I.In this paper, the mechanical systems with fractional derivatives are studied by using fractional formalism. The path integral quantization of these system is constructed as an integration over the canonical phase space. The path integral quantization of a system with Brownian motion is carried out. Copyright 2006 IFAC.Article Citation - WoS: 24Citation - Scopus: 34Coupled Transform Method for Time-Space Fractional Black-Scholes Option Pricing Model(Elsevier, 2020) Jena, R. M.; Chakraverty, S.; Baleanu, D.; Edeki, S. O.This paper presents analytical solutions of a time-space-fractional Black-Scholes model (TSFBSM) using a coupled technique referred to as Fractional Complex Transform (FCT) with the aid of a modified differential transform method. The nature of the derivatives is in the sense of Jumarie. The considered cases and applications show more consistency of the TSFBSM with an actual integer and fractional data when compared with the classical Black-Scholes model. The method is noted to be very effective, even with little knowledge of fractional calculus. Extension of this to multi-factor models formulated in terms of stochastic dynamics is highly recommended. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.Article Citation - WoS: 134Citation - Scopus: 154A New Approach for Solving Multi Variable Orders Differential Equations With Mittag-Leffler Kernel(Pergamon-elsevier Science Ltd, 2020) Jafari, H.; Baleanu, D.; Ganji, R. M.In this paper we consider multi variable orders differential equations (MVODEs) with non-local and no-singular kernel. The derivative is described in Atangana and Baleanu sense of variable order. We use the fifth-kind Chebyshev polynomials as basic functions to obtain operational matrices. We transfer the original equations to a system of algebraic equations using operational matrices and collocation method. The convergence analysis of the presented method is discussed. Few examples are presented to show the efficiency of the presented method. (C) 2019 Elsevier Ltd. All rights reserved.Article Citation - WoS: 9Citation - Scopus: 11A New Glance on the Leibniz Rule for Fractional Derivatives(Elsevier Science Bv, 2018) Machado, J. Tenreiro; Baleanu, D.; Sayevand, K.; Tenreiro Machado, J.This paper proposes a new strategy to study some useful properties of growth rates of functions in C-alpha is an element of R spaces in order to analyze the Leibniz rule for fractional derivatives. The differential operators are taken in the Riemann-Liouville sense. Moreover, stability analysis of the proposed strategy is investigated. The results demonstrate that the proposed theoretical analysis is accurate. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 35Citation - Scopus: 40Shifted Chebyshev Schemes for Solving Fractional Optimal Control Problems(Sage Publications Ltd, 2019) Moussa, H.; Baleanu, D.; El-Kady, M.; Abdelhakem, M.Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.